Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
386 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #27133217 | C2 | semidirect |
| 3. #27132959 | C2 | semidirect |
| 4. #27132958 | C2 | semidirect |
| 5. #27132941 | C2 | semidirect |
| 6. #27132908 | C2 | semidirect |
| 7. #27132906 | C2 | semidirect |
| 8. #27132866 | C2 | semidirect |
| 9. #27132860 | C2 | semidirect |
| 10. #27132685 | C2 | semidirect |
| 11. #460×C191 | C2 | semidirect |
| 137. C191 | #3254 | semidirect |
| 148. #460 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133217 | 2 |
| #27133211 | 2 |
| #27132959 | 2 |
| #27132958 | 2 |
| #27132941 | 2 |
| #27132908 | 2 |
| #27132906 | 2 |
| #27132866 | 2 |
| #27132860 | 2 |
| #27132685 | 2 |
| #460×C191 | 2 |
| #3254 | 191 |